You can use this for the forgot password component , carrer login page (applicant login) or any other similar pages strighat way.

Following are modified steps from the reCAPTCHA website for the PeopleSoft Implementation.

First, go to the reCAPTCHA web site and create an account. As part of that account creation process you'll have to specify the domain your reCAPTCHA will be protecting. The reCAPTCHA site will will give you a key pair for that domain. The key pair allows you to authenticate your reCAPTCHA requests to the reCAPTCHA servers

Second, Create the HTML Area in the PeopleSoft page where you want the ReCaptcha to apper
in the HTML Defination add the follwing Java script code, you need to enclose it with form tags.
make sure you replace - with the public key from the key pair created in reCaptcha website.
Download the Java API library in the following location

Add button on the page, similar to submit button for the page, on field change of the button you can write the code as below.
PS: Make sure you replace the private in code with the private key generated by reCaptcha for your domain.
Hope this will be helpfull.